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"Decomposition (Mathematics)"
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The driving forces of change in environmental indicators : an analysis based on divisia index decomposition techniques
This book addresses several index decomposition analysis methods to assess progress made by EU countries in the last decade in relation to energy and climate change concerns. Several applications of these techniques are carried out in order to decompose changes in both energy and environmental aggregates. In addition to this, a new methodology based on classical spline approximations is introduced, which provides useful mathematical and statistical properties. Once a suitable set of determinant factors has been identified, these decomposition methods allow the researcher to quantify the respective contributions of these factors. A proper interpretation of findings enables the design of strategies and a number of energy and environmental policies to control the variables of interest. This book also analyses the impact of several factors that allow control of these variables; among them, assessment of the specific contribution of improved energy efficiency is particularly relevant. A number of divisia-index-based techniques for decomposing changes in a generic indicator are now available, and these range from classical techniques based on Laspeyres and Paasche weights to more refined approaches relying on logarithmic mean weighting schemes. This book is intended for undergraduates and graduates of energy economics and environmental sciences, environmental policy advisors, and industrial engineers.
Book
Proof of the 1-factorization and Hamilton Decomposition Conjectures
In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D\\geq 2\\lceil n/4\\rceil -1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, \\chi'(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D \\ge \\lfloor n/2 \\rfloor . Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree \\delta\\ge n/2. Then G contains at least {\\rm reg}_{\\rm even}(n,\\delta)/2 \\ge (n-2)/8 edge-disjoint Hamilton cycles. Here {\\rm reg}_{\\rm even}(n,\\delta) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree \\delta. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case \\delta= \\lceil n/2 \\rceil of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.
eBook
The Existence of Designs via Iterative Absorption: Hypergraph 𝐹-designs for Arbitrary
We solve the existence problem for
Our main result concerns decompositions of hypergraphs whose clique distribution fulfills certain regularity
constraints. Our argument allows us to employ a ‘regularity boosting’ process which frequently enables us to satisfy these constraints
even if the clique distribution of the original hypergraph does not satisfy them. This enables us to go significantly beyond the setting
of quasirandom hypergraphs considered by Keevash. In particular, we obtain a resilience version and a decomposition result for
hypergraphs of large minimum degree.
eBook
IS FULLY P.sub.7, S.sub.4-DECOMPOSABLE
Let Pk+1 denote a path of length k, [S.sub.m] denote a star with m edges, and [K.sub.n] ([lambda]) denote the complete multigraph on n vertices in which every pair of distinct vertices is joined by [lambda] edges. In this paper, we have obtained the necessary conditions for a Pk+1, Sm-decomposition of [K.sub.n]([lambda]) and proved that the necessary conditions are also sufficient when k = 6 and m = 4. Keywords: Decomposition, Complete multigraph, Path, Star. AMS Subject Classification: 05C70, 05C38.
Journal Article
Solutions of Time Fractional
The current study employs the natural transform decomposition method (NTDM) to test fractional-order partial differential equations (FPDEs). The present technique is a mixture of the natural transform method and the Adomian decomposition method. For the purpose of checking the precis of our technique, some examples are offered, and the series solutions of these equations are introduced by using NTDM. The outcome shows that the suggested approach is very active and straightforward for obtaining a series solutions of FPDEs and is more accurate if we compare it with existing methods.
Journal Article
On Sudakov’s type decomposition of transference plans with norm costs
We consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost
In this paper we show
how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented.
The results yield
a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the
Monge problem in each set
The analysis requires
(1)
(2)
(3)
(4)
eBook
Bi-Squashing Ssub.2,2-Designs into -Designs
A double-star S[sub.q1,q2] is the graph consisting of the union of two stars, K[sub.1,q1] and K[sub.1,q2] , together with an edge joining their centers. The spectrum for S[sub.q1,q2] -designs, i.e., the set of all the n∈N such that an S[sub.q1,q2] -design of the order n exists, is well-known when q[sub.1] =q[sub.2] =2. In this article, S[sub.2,2] -designs satisfying additional properties are investigated. We determine the spectrum for S[sub.2,2] -designs that can be transformed into (K[sub.4] −e)-designs by a double squash (bi-squash) passing through middle designs whose blocks are copies of a bull (the graph consisting of a triangle and two pendant edges). Here, the use of the difference method enables obtaining cyclic decompositions and determining the spectrum for cyclic S[sub.2,2] -designs that can be purely bi-squashed into cyclic (K[sub.4] −e)-designs (the middle bull designs are also cyclic).
Journal Article
On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs
We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of stochastic dual dynamic programming, cutting-plane and partial-sampling (CUPPS) algorithm, and dynamic outer-approximation sampling algorithms when applied to problems with general convex cost functions.
Journal Article
Spectral proper orthogonal decomposition using multitaper estimates
The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the standard SPOD algorithm that exclusively relies on weighted overlapped segment averaging, or Welch’s method, to estimate the cross-spectral density matrix. Two sets of turbulent flow data, one experimental and the other numerical, are used to discuss the choice of resolution bandwidth and the bias-variance tradeoff. Multitaper-Welch estimators that combine both approaches by applying orthogonal tapers to overlapping segments allow for flexible control of resolution, variance, and bias. At additional computational cost but for the same data, multitaper-Welch estimators provide lower variance estimates at fixed frequency resolution or higher frequency resolution at similar variance compared to the standard algorithm.Graphic abstract
Journal Article
Offline and online coupled tensor factorization with knowledge graph
How can we accurately decompose a temporal irregular tensor along while incorporating a related knowledge graph tensor in both offline and online streaming settings? PARAFAC2 decomposition is widely applied to the analysis of irregular tensors consisting of matrices with varying row sizes. In both offline and online streaming scenarios, existing PARAFAC2 methods primarily focus on capturing dynamic features that evolve over time, since data irregularities often arise from temporal variations. However, these methods tend to overlook static features, such as knowledge-based information, which remain unchanged over time. In this paper, we propose KG-CTF ( K nowledge Graph-based Coupled Tensor Factorization) and OKG-CTF ( O nline Knowledge Graph-based Coupled Tensor Factorization), two coupled tensor factorization methods designed to effectively capture both dynamic and static features within an irregular tensor in offline and online streaming settings, respectively. To integrate knowledge graph tensors as static features, KG-CTF and OKG-CTF couple an irregular temporal tensor with a knowledge graph tensor by sharing a common axis. Additionally, both methods employ relational regularization to preserve the structural dependencies among the factor matrices of the knowledge graph tensor. To further enhance convergence speed, we utilize momentum-based update strategies for factor matrices. Through extensive experiments, we demonstrate that KG-CTF reduces error rates by up to 1.64× compared to existing PARAFAC2 methods. Furthermore, OKG-CTF achieves up to 5.7× faster running times compared to existing streaming approaches for each newly arriving tensor.
Journal Article